On Clique Sombor Index of Graphs and Their Properties

We introduce the Clique Sombor index (CS index), a new degree-based topological index defined using the vertex clique degree of a graph. Basic bounds and relations with classical indices are established. Exact formulas are derived for standard graphs such as paths, cycles, complete graphs, complete bipartite graphs, wheels, ladders, friendship graphs, windmill graphs, Dutch windmill graphs, and grids. Closed expressions are also obtained for cactus chains, including triangle chains, para-chain square cacti, ortho-chain hexagon cacti, and para-chain hexagon cacti. The results highlight the mathematical richness of the CS index and its potential applications in QSPR and QSAR studies.